4050
Langmuir 2005, 21, 4050-4057
Surface Enzyme Kinetics for Biopolymer Microarrays: a
Combination of Langmuir and Michaelis-Menten Concepts
Hye Jin Lee, Alastair W. Wark, Terry T. Goodrich, Shiping Fang, and
Robert M. Corn*
Department of Chemistry, University of California-Irvine, Irvine, California 92697
Received December 21, 2004. In Final Form: February 14, 2005
Real-time surface plasmon resonance (SPR) imaging measurements of surface enzymatic reactions on
DNA microarrays are analyzed using a kinetics model that couples the contributions of both enzyme
adsorption and surface enzyme reaction kinetics. For the case of a 1:1 binding of an enzyme molecule (E)
to a surface-immobilized substrate (S), the overall enzymatic reaction can be described in terms of classical
Langmuir adsorption and Michaelis-Menten concepts and three rate constants: enzyme adsorption (ka),
enzyme desorption (kd) and enzyme catalysis (kcat). In contrast to solution enzyme kinetics, the amount
of enzyme in solution is in excess as compared to the amount of substrate on the surface. Moreover, the
surface concentration of the intermediary enzyme-substrate complex (ES) is not constant with time, but
goes to zero as the reaction is completed. However, kinetic simulations show that the fractional surface
coverage of ES on the remaining unreacted sites does reach a steady-state value throughout the course
of the surface reaction. This steady-state value approaches the Langmuir equilibrium value for cases
where ka[E] . kcat. Experiments using the 3′ f 5′ exodeoxyribonuclease activity of Exonuclease III on
double-stranded DNA microarrays as a function of temperature and enzyme concentration are used to
demonstrate how this model can be applied to quantitatively analyze the SPR imaging data.
I. Introduction
The parallel enzymatic processing of biopolymer microarrays is rapidly becoming an integral component in
the creation of many novel surface-based biotechnologies
and bioaffinity sensor applications. Enzymes are attractive
tools for surface bioengineering for a number of reasons:
surface enzyme reactions are highly specific and result in
selective surface site modifications, work under biocompatible conditions often with high efficiency, and in some
cases, are reversible. For example, we have recently
demonstrated the use of RNase H to enzymatically amplify
the signal in surface plasmon resonance (SPR) imaging
measurements on nucleic acid microarrays and have also
used SPR imaging to monitor the cleavage of peptide
arrays with the enzyme Factor Xa.1,2 Other researchers
have used single-base-extension enzyme reactions on DNA
microarrays to detect single nucleotide polymorphisms
(SNPs).3 In addition to biosensing applications, the
implementation of DNA computing algorithms on surfaces
also requires the processing of immobilized oligonucleotides with various DNA enzymes.4 Directed enzymatic
cleavage of an oligonucleotide monolayer has also been
applied to create nanometer-scale surface patterns.5,6
A simple reaction scheme for the enzymatic processing
of surface biopolymers is shown in Figure 1. The enzyme
(E) first adsorbs from solution onto the surface-bound
* Author to whom correspondence should be addressed. E-mail:
[email protected].
(1) Goodrich, T. T.; Lee, H. J.; Corn, R. M. Anal. Chem. 2004, 76,
6173-6178.
(2) Wegner, G. J.; Wark, A. W.; Lee, H. J.; Codner, E.; Saeki, T.;
Fang, S.; Corn, R. M. Anal. Chem. 2004, 76, 5677-5684.
(3) Giusto, D. D.; King, G. C. Nucl. Acids Res. 2003, 31, e7.
(4) Frutos, A. G.; Condon, A. E.; Smith, L. M.; Corn, R. M. J. Am.
Chem. Soc. 1998, 120, 10277-10282.
(5) Jang, C.; Stevens, B. D.; Carlier, P. R.; Calter, M. A.; Ducker, W.
A. J. Am. Chem. Soc. 2002, 124, 12114-12115.
(6) Hyun, J.; Kim, J.; Craig, S. L.; Chilkoti, A. J. Am. Chem. Soc.
2004, 126, 4770-4771.
Figure 1. A reaction scheme showing the surface enzymatic
processing of a biopolymer microarray.
substrate (S) to create the surface complex (ES). The
surface complex then reacts to form the surface-bound
product (S*). This reaction scheme differs from the typical
enzymatic method for detecting species on surfaces, which
uses a sandwich assay in which an enzyme-protein
conjugate binds to an adsorbed molecule and then reacts
with a substrate in solution to create an amplified detection
signal (optical, electrochemical, etc.).7,8 In contrast, the
substrate in the enzyme reaction scheme presented in
Figure 1 is surface-bound and therefore limited in number
as compared to the enzyme in solution. Moreover, the
reaction of the surface enzyme complex releases the
enzyme back into solution.
Despite the attractive features of enzymes as surface
biochemical tools, there are to date very few researchers
that have quantitatively considered the kinetics and
thermodynamics of enzyme-catalyzed surface reactions.
(7) Crowther, J. R. ELISA: Theory and Practice, 1st ed.; Humana
Press Inc.: Totowa, NJ, 1995; Vol. 42.
(8) Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J. J. Am. Chem.
Soc. 1999, 121, 2401-2408.
10.1021/la046822h CCC: $30.25 © 2005 American Chemical Society
Published on Web 03/22/2005
Surface Enzyme Kinetics for Biopolymer Microarrays
In a series of papers, Gast et al. have examined the reaction
of collagenase on peptide monolayers9-11 and the reaction
of protease on BSA monolayers.12 For the case of protease adsorption and reaction, they proposed a modified
Michaelis-Menten model for the surface kinetics. However, the authors restricted their kinetic analysis to the
later stage of the reaction with over 75% of the substrate
removed.12 For this time regime, the adsorption kinetics
and surface enzyme reaction are decoupled.
To study surface enzymatic reaction rates quantitatively, various analytical approaches have been employed
to directly monitor the surface process in real-time and
discriminate against possible bulk signal contribution.
While most research efforts have focused on the use of
fluorescence-based detection methods,9,10,13-16 SPR-based
techniques have recently gained more attention due to
the distinct advantage of being “label-free” such that the
inconvenience and potential alteration of biological activity
associated with fluorescent tags is avoided.1,2,17-22 For
example, Robertson et al.12 have employed a combination
of SPR and surface plasmon enhanced fluorescence to
create separate profiles of the enzyme adsorption and
substrate cleavage steps. In addition, we have demonstrated that time-resolved SPR imaging measurements
can be used to study Langmuir adsorption kinetics and
enzyme reaction kinetics on surfaces.2
In this paper, we propose a novel approach to the
quantitative analysis of enzyme-catalyzed surface reactions that couples both adsorption kinetics and enzyme
kinetics to quantitatively describe the reaction of an
enzyme in solution with a surface-immobilized substrate.
We find that the surface coverage of the enzyme-substrate
intermediate is governed by an interesting combination
of classical Langmuir adsorption kinetics and MichaelisMenten concepts. As an example, we investigate the
exodeoxyribonuclease activity of Exonuclease III on wellcharacterized double-stranded DNA (dsDNA) microarrays.23,24 The kinetics of the selective 3′ f 5′ Exo III
hydrolysis of one strand of the two DNA strands in a DNA
duplex was monitored at various temperatures using the
multiplexed technique of real-time SPR imaging.1,2 For
the Exo III surface reaction at 20 °C, the SPR signal
initially increaseddue to enzyme adsorption and then
(9) Gaspers, P. B.; Robertson, C. R.; Gast, A. P. Langmuir 1994, 10,
2699-2704.
(10) Gaspers, P. B.; Gast, A. P.; Robertson, C. R. J. Colloid Interface
Sci. 1995, 172, 518-529.
(11) Trigiante, G.; Gast, A. P.; Robertson, C. R. J. Colloid Interface
Sci. 1999, 213, 81-86.
(12) Kim, J.; Roy, S.; Kellis, J. T., Jr.; Poulose, A. J.; Gast, A. P.;
Robertson, C. R. Langmuir 2002, 18, 6312-6318.
(13) Jervis, E. J.; Haynes, C. A.; Kilburn, D. G. J. Biol. Chem. 1997,
272, 24016-24023.
(14) Tachi-iri, Y.; Ishikawa, M.; Hirano, K. Anal. Chem. 2000, 72,
1649-1656.
(15) Bosma, A. Y.; Ulijn, R. V.; McConnell, G.; Girkin, J.; Hallingc,
P. J.; Flitsch, S. L. Chem. Commun. 2003, 22, 2790-2791.
(16) Tawa, K.; Knoll, W. Nucl. Acids Res. 2004, 32, 2372-2377.
(17) Peterson, A. W.; Wolf, L. K.; Georgiadis, R. M. J. Am. Chem. Soc.
2002, 124, 14601-14607.
(18) Goodrich, T. T.; Lee, H. J.; Corn, R. M. J. Am. Chem. Soc. 2004,
126, 4086-4087.
(19) Shumaker-Parry, J. S.; Campbell, C. T. Anal. Chem. 2004, 76,
907-917.
(20) Shumaker-Parry, J. S.; Zareie, M. H.; Aebersold, R.; Campbell,
C. T. Anal. Chem. 2004, 76, 918-929.
(21) Kyo, M.; Yamamoto, T.; Motohashi, H.; Kamiya, T.; Kuroita, T.;
Tanaka, T.; Engel, J. D.; Kawakami, B.; Yamamoto, M. Genes Cells
2004, 9, 153-164.
(22) Kanda, V.; Kariuki, J. K.; Harrison, D. J.; McDermott, M. T.
Anal. Chem. 2004, 76, 7257-7262.
(23) Nelson, B. P.; Grimsrud, T. E.; Liles, M. R.; Goodman, R. M.;
Corn, R. M. Anal. Chem. 2001, 73, 1-7.
(24) Lee, H. J.; Goodrich, T. T.; Corn, R. M. Anal. Chem. 2001, 73,
5525-5531.
Langmuir, Vol. 21, No. 9, 2005 4051
decreased as the surface exonuclease reaction went to
completion. This real-time SPR response was monitored
at various bulk enzyme concentrations and analyzed using
the proposed surface kinetic model to achieve further
insight into the relative contributions of the enzyme
adsorption and catalytic steps to the overall reaction rate.
II. Theoretical Considerations
Figure 1 depicts a reaction scheme for the surface
enzymatic processing of a biopolymer microarray where
the enzyme binds specifically to an immobilized substrate
molecule in a simple 1:1 ratio. In the absence of bulk
transport limitations, the reaction steps can be represented in the form:
ka
S + E {\
} ES
k
d
kcat
ES 98 S* + E
(1)
(2)
where S is the surface bound substrate, E is the enzyme
in solution, ES is the surface bound enzyme-substrate
complex, and S* is the surface bound product. Assuming
that enzyme adsorption and desorption are described by
simple Langmuir kinetics, the reaction rates for the
production of ES and S* can be given by eqs 3 and 4:
dΓES
) kaΓS[E] - kdΓES - kcatΓES
dt
(3)
dΓS*
) kcatΓES
dt
(4)
where Γ denotes a surface coverage. If Γtot is the total
number of surface sites, then the reaction rates can be
expressed in terms of the relative surface coverages, θx )
Γx/Γtot, where x ) S, ES or S*:
θS + θES + θS* ) 1
(5)
dθES
) kaθS[E] - kdθES - kcatθES
dt
(6)
dθS*
) kcatθES
dt
(7)
The solution of the coupled surface kinetics eqs 6 and 7
depends on the relative values of the rate constants ka, kd,
and kcat.
A. Steady-State Solution for Slow Surface Enzyme
Kinetics. If the surface enzyme reaction is very slow as
compared to the adsorption process (kcat , ka,kd), then we
can assume that surface coverage of the intermediate ES
is constant (dθES/dt ) 0) and we can solve eq 6 for θES:
θES )
kaθS[E]
θS[E]
)
kd + kcat
K′M
(8)
where K′M is defined as the “surface” Michaelis-Menten
constant:
K′M )
kd + kcat
ka
(9)
4052
Langmuir, Vol. 21, No. 9, 2005
Lee et al.
This definition is analogous to the definition of the normal
solution Michaelis-Menten constant.25 Initially, the
amount of product, S*, on the surface is small and can be
neglected in eq 5. We define θ′ES as the steady-state
surface coverage of the intermediate ES for this case. Using
eq 5 to replace θS in eq 8 with 1 - θ′ES leads to the following
equation:
θ′ES )
[E]
K′M + [E]
(10)
Equation 10 has the same functional form as that observed
in solution Michaelis-Menten enzyme kinetics, [ES]/Etot
) [S]/(KM + [S]),25 but the surface reaction rate is a function
of solution enzyme concentration ([E]) instead of surface
substrate concentration ([S]). This is because, in the
solution reaction, the substrate is typically in excess
relative to the enzyme, whereas for surface enzyme
kinetics, the enzyme in solution is in excess relative to the
substrate on the surface.
Equation 10 can also be described as a “dynamic”
Langmuir adsorption isotherm for the surface enzyme
complex. If kcat is much smaller than kd, then the surface
Michaelis-Menten constant, K′M, in eq 9 becomes the
inverse of the Langmuir adsorption coefficient, KAds ) ka/
kd, and eq 10 becomes the normal equilibrium Langmuir
adsorption isotherm and the surface coverage reaches its
equilibrium value (θeq
ES):
θeq
ES
)
KAds[E]
1 + KAds[E]
if kcat , kd
(11)
Thus, we find that the initial rate of the surface enzyme
reaction is proportional to the steady-state coverage of
the intermediate ES, and the inverse of the surface
Michaelis-Menten constant can be thought of as a
“dynamic” Langmuir adsorption coefficient that controls
the ES surface coverage. If the reaction is very slow, then
this steady-state surface coverage is the same as the
equilibrium ES surface coverage as given by the Langmuir
adsorption isotherm.
B. General Solution and Surface Simulations. If
kcat is equal to or greater than ka[E], then we cannot make
the steady-state assumption that the surface ES concentration is constant and the surface S* concentration is
negligible. Instead, kinetic simulations of eqs 6 and 7 must
be used to follow the temporal evolution of the relative
surface coverages during the course of the enzymatic
reaction.
The kinetic simulations are easily performed using
Euler integration methods with the initial conditions that
θS ) 1, θES ) 0, and θS* ) 0 at time t ) 0 (we actually
reduce the problem to only two variables by eliminating
θS from eq 6 by using eq 5). An example of a kinetic
simulation is shown in Figure 2 where kcat and ka[E] are
arbitrarily set equal to 0.25 s-1 and kd is set to 0.025 s-1.
As seen in this figure, the surface coverage of S (θS) drops
monotonically to zero as the relative surface coverage of
the product S* (θS*) monotonically increases to one as the
reaction is completed. The relative surface coverage of
the intermediate ES (θES) is not constant during the course
of the reaction but instead rises to a maximum value of
0.38 after ∼4 s, and then slowly decreases to zero. It never
(25) Copeland, R. A. Enzymes: A practical introduction to structure,
mechanism and data analysis; Wiley-VCH: New York, 2000; Vol. 2, pp
109-145.
Figure 2. Kinetic simulation of the surface enzyme reactions
defined in eqs 5-7. For this simulation, ka[E] ) kcat ) 0.25 s-1;
kd ) 0.025 s-1. The steady-state value for λES is 0.728.
Figure 3. Kinetic simulation of the surface enzyme reactions
defined in eqs 5-7. For this simulation, ka[E] ) 0.25 s-1; kcat
) kd ) 0.025 s-1. The steady-state value for λES is 0.901.
achieves its equilibrium value of θeq
ES ) 0.909, as determined from the Langmuir isotherm (eq 11).
The surface coverage of ES is not constant during the
course of this reaction because the surface is rapidly being
converted to the final product, S*. However, the surface
coverage of both the intermediate ES and the total number
of unreacted sites are decreasing with time at the same
rate. To show this, we also plot in Figure 2 the fraction
of unreacted surface sites that are occupied by the enzyme,
which we define as λES:
λES )
θES
θES
)
θES + θS 1 - θS*
(12)
Surprisingly, in Figure 2, λES rises to a steady-state value
of 0.728 that does not change as the surface is depleted.
This steady-state value is below that of the equilibrium
value of 0.909. If we make kcat 10 times smaller, the kinetic
simulation changes as shown in Figure 3. The relative
surface coverage of ES rises to a value of 0.7 and then
decreases at considerably slower rate than that shown in
Figure 2. However, λES rises close to the steady-state
Langmuir isotherm equilibrium value and remains constant.
The dependence of the steady-state value of λES on both
kcat and ka[E] can be determined analytically. The rate of
change of λES can be written as
θES
dθES
dθS*
dλES
1
)
+
2
dt
1 - θS* dt
(1 - θS*) dt
(13)
To find the steady-state value of λES, eq 13 is set to zero
and after solving for λES yields
λES ) -
[( )]
dθES dθS*
dt
dt
-1
(14)
Surface Enzyme Kinetics for Biopolymer Microarrays
Langmuir, Vol. 21, No. 9, 2005 4053
where β is a dimensionless parameter:
β)
Figure 4. Variation in the steady-state value of λES as a function
of log kcat with the values of ka[E] ) 0.25 s-1 and kd ) 0.025 s-1.
(O) represents the value of λES (0.728) when kcat ) ka[E] ) 0.25
s-1 and (0) shows the value of λES (0.901) when kcat < ka[E] with
kcat ) 0.025 s-1.
Substitution of eqs 6 and 7 into eq 14 yields after
rearrangement:
λES ) -
ka[E]
(ka[E] + kd + kcat)
+
kcatλES
kcat
(15)
Equation 15 is a quadratic equation for λES which can be
solved with the quadratic formula using the appropriate
root to yield the steady-state value of λES observed in the
kinetic simulations. Figure 4 plots the variation in λES
obtained using eq 15 as a function of kcat with fixed values
of ka[E] ) 0.25 s-1 and kd ) 0.025 s-1. The steady-state
value of λES depends on the relative values of kcat, ka[E],
and kd. Note that, as kcat decreases, λES approaches the
Langmuir equilibrium value of 0.909. When kcat is equal
to ka[E], a steady-state value of λES ) 0.728 is obtained,
which is exactly the value observed in Figure 2. As kcat
becomes larger than ka[E], λES approaches zero. If kcat is
much larger than ka[E], the velocity of the surface enzyme
reaction will be solely limited by the enzyme adsorption
kinetics. These equations demonstrate that, just as in the
simple case when kcat is small, there is a dynamic steadystate equilibrium set up for ES. However, it is the
fractional surface coverage of ES relative to the number
of unreacted sites (λES) that remains constant, even as the
total number of unreacted sites (θES) goes to zero as the
surface reaction is completed.
C. Diffusion Contributions to the Surface Enzymatic Reaction. In the kinetic analysis described above,
we have not yet considered the possibility that enzyme
diffusion to the gold surface may have an influence on the
time-resolved SPR signal. Specifically, if diffusion is important, the bulk enzyme concentration [E] in eq 6 should
be replaced by the enzyme concentration at the surface.
The effect of diffusion on Langmuir adsorption and desorption kinetics has been examined in detail in the SPR
literature26-29 and in related electrochemical literature.8,30
For the case of a microfluidic flow cell such as the one
used in our SPR kinetics measurements, a steady-state
diffusion layer of thickness δ is created and eq 6 must be
modified. In the absence of catalytic activity (kcat ) 0),
diffusion contributions to the rate of enzyme adsorption
can be included using the following differential equation:8
dθES ka[E](1 - θES) - kdθES
)
dt
1 + β(1 - θES)
(16)
(26) Karlsson, R.; Roos, H.; Fagerstam, L.; Persson, B. Methods 1994,
6, 99-110.
(27) Schuck, P.; Minton, A. P. Anal. Biochem. 1996, 240, 262-272.
(28) Myszka, D. G. Curr. Opin. Biotechnol. 1997, 8, 50-57.
(29) Myszka, D. G.; He, X.; Dembo, M.; Morton, T. A.; Goldstein, B.
Biophys. J. 1998, 75, 583-594.
(30) Bhugun, I.; Anson, F. C. J. Electroanal. Chem. 1997, 439, 1-6.
kaΓtotδ kaΓtot
)
D
km
(17)
which compares the rate of adsorption to the rate of
diffusion, where D is the diffusion constant for the enzyme
and km ) D/δ is the mass transfer coefficient. We can
rederive this equation to include catalytic activity (kcat *
0):
dθES ka[E](1 - θES - θS*) - kdθES - kcatθES
)
dt
1 + β(1 - θES - θS*)
(18)
Equation 18 can be used as a direct replacement for eq
6.
Equation 16 has been derived previously by Saveant et
al.8 for rotating disk electrodes and by Shuck and Minton
27
using a “two compartment model”. This model is used
frequently in the SPR literature to include any diffusion
contributions.29 To experimentally confirm that there is
a diffusion contribution, it is necessary to measure the
flow-rate dependence of the SPR response.31 If there is a
flow rate dependence, eq 16 can be integrated and the
SPR adsorption curves can be analyzed to determine the
Langmuir adsorption coefficient. If there is no flow-rate
dependence of the SPR response, the effects of diffusion
can be ignored and the adsorption coefficient can be
ascertained from the standard equations for Langmuir
adsorption kinetics.2
For all of the Exo III surface enzyme kinetics examined
in this paper at various enzyme concentrations and
reaction temperatures, no significant changes in the SPR
response were observed for flow rates from 30 to 1000
µL/min. This indicates that mass transport has a negligible
role in determining the overall reaction rate under our
experimental conditions.
A second method for examining possible diffusion
contributions is to use eq 17 to estimate the parameter β.
With a molecular weight of 28 000 Da, the Exo III diffusion
coefficient can be estimated32 to be 10-6 cm2‚s-1. Assuming
a diffusion layer thickness of 5 µm26 and a double-stranded
DNA (dsDNA) surface coverage of 5 × 10-13 moles‚cm-2,
we find that β ) 10-7ka. Subsequent data analysis indicates
a ka value for Exo III binding to be close to 105 M-1‚s-1,
suggesting a value of 0.01 for β. This small value for β
agrees with our experimental finding that the SPR
response did not change with flow rate.
A second diffusion contribution that is neglected in this
kinetic analysis is any lateral diffusion of the enzyme along
the surface prior to complexation. In some enzyme systems,
adsorption to the surface can occur without complexation
to the substrate. This was the case for the system studied
by Gast et al.12 However, for Exo III, adsorption was never
observed on control array elements where the dsDNA
substrate was absent. We therefore do not include a surface
population of adsorbed but uncomplexed enzymes in our
kinetic equations nor any contributions due to lateral
diffusion of adsorbed but uncomplexed enzymes on the
surface.
III. Experimental Section
Materials. 11-Mercaptoundecylamine (MUAM; Dojindo), sulfosuccinimidyl 4-(N-maleimidomethyl)-cyclohexane-1-carboxylate (SSMCC; Pierce), 9-fluorenylmethoxycarbonyl-N-hydroxy(31) Myszka, D. G.; Morton, T. A.; Doyle, M. L.; Chaiken, I. M. Biophys.
Chem. 1997, 64, 127-137.
(32) Christensen, L. L. H. Anal. Biochem. 1997, 249, 153-164.
4054
Langmuir, Vol. 21, No. 9, 2005
succinimide (Fmoc-NHS; Novabiochem), N-hydroxysuccinimidyl
ester of methoxypoly(ethylene glycol) propionic acid (PEG-NHS;
Nektar; MW 2000), and Exonuclease III (Exo III; Promega; 1
U/mL ) 0.17 nM) were all used as received. Tris buffer (50 mM
Tris-HCl, 10 mM MgCl2, pH 7.4) was used for all Exo III
experiments. All of either 5′ or 3′ thiol-modified DNA oligonucleotides were purchased from IDT (Integrated DNA Technologies) and were purified and deprotected using binary reversephase HPLC. The complementary DNA (HPLC purified) was
obtained commercially from IDT (Integrated DNA Technologies).
The DNA oligonucleotides used in these experiments are as
follows: D1 ) 3′ S-S(CH2)3A20, D2 ) 5′ S-S(CH2)6T20 and C1 )
5′(T)20. All rinsing steps were performed with absolute ethanol
and Millipore filtered water.
DNA Array Fabrication. A multistep chemical modification
process was used to fabricate DNA microarrays for SPR imaging
experiments and can be found elsewhere.23,33 Briefly, thin gold
films (45 nm) with an underlayer of chromium (1 nm) were
deposited onto SF-10 glass (Schott Glass) using a Denton DV502A metal evaporator. The gold substrate was reacted to form
a self-assembled monolayer (SAM) of an amine-terminated
alkanethiol MUAM. The amine-terminated SAM was then
reacted with the temporary hydrophobic protecting group FmocNHS. By exposing the surface to UV radiation through a quartz
mask containing 500 µm × 500 µm features, patterns of bare
gold spots surrounded by the hydrophobic background were
created. The bare gold spots were then modified with MUAM
and spotted with the heterobifunctional cross-linker SSMCC to
form a thiol-reactive maleimide-terminated surface. Thiolmodified sequences of DNA were then spotted into these
hydrophilic array elements using a pneumatic picopump. To avoid
the nonspecific adsorption of enzyme and cleaved product, the
Fmoc background was replaced with poly(ethylene glycol) (PEG)
after deprotection. The surface coverage of the single-stranded
DNA (ssDNA) monolayer was estimated to be approximately 1
× 1012 molecules/cm2.
Kinetic Flow Cell Design. A PDMS microfluidics system
previously developed2 was used to continuously deliver small
sample volumes onto an array surface for kinetics measurements.
Briefly, a serpentine PDMS microchannel (670 µm width, 9.5 cm
length, 200 µm depth, total volume ≈ 10 µL) was pretreated with
oxygen plasma for 10 s and placed in direct contact with the
array surface. Oxygen plasma treatment enhances the hydrophilicity of the PDMS channels thus facilitating the introduction
of aqueous samples, as well as reducing biomolecular adsorption
onto the walls of the channels. A constant temperature sample/
prism holder was used in conjunction with the microfluidics in
order to reduce any fluctuations in SPR signal over time due to
temperature variations. The details of the constant temperature
cell can be found elsewhere.1,2 Buffer and/or sample solutions
were introduced to the array using a syringe pump at a constant
flow rate of 30 µL/min.
Real-Time SPR Imaging Measurements. An SPR imaging
apparatus (GWC Technologies) was used for the real-time
monitoring of the hydrolysis of DNA microarrays by Exo III.
Briefly, a collimated p-polarized light at a fixed angle reflected
from the sample/gold/prism assembly is sent through a narrow
band-pass filter and then detected with a CCD camera. The data
are collected using the software package V++ (Digital Optics,
NZ). Custom macros were written using this software so that
data could be collected with simultaneous processing of several
specific user designated regions of interest (ROIs) on the array
surface.2 All kinetics experiments presented in this paper were
obtained by collecting one data point for each ROI approximately
every 1 s that was the average of five camera frames. The
difference in percent reflectivity for each probe area was
normalized with respect to the average change in percent
reflectivity measured for the PEG background and negative
control ROIs. This helps account for changes in the SPR signal
due to miscellaneous factors such as slight temperature variations
and bulk refractive index changes. Kinetic data from multiple
identical array elements were averaged to obtain the final SPR
response curves. Microsoft Excel and Igor Pro were used for all
data processing and kinetic model fitting in these experiments.
(33) Brockman, J. M.; Frutos, A. G.; Corn, R. M. J. Am. Chem. Soc.
1999, 121, 8044-8051.
Lee et al.
Figure 5. (a) Schematic representation of 3′ f 5′ exodeoxyribonuclease activity of Exo III specific for double-stranded DNA
microarrays. (b) An SPR difference image showing the sequence
specific hybridization adsorption of 500 nM complementary
DNA (C1) onto D1 array elements. (c) An SPR difference image
obtained after an 80 nM solution of Exo III is introduced to
the DNA microarray shown in (b) for 40 min. (d) The pattern
used to create a two-component DNA microarray using thiolmodified DNA sequences (D1 and D2). Array elements are 500
µm × 500 µm squares. Probe D1 was designed to bind to the
target DNA C1, and probe sequence D2 was chosen as a negative
control.
IV. Results and Discussion
A. Exonuclease III Specificity. Exo III is widely used
in various DNA manipulative procedures such as DNA
repair, site-directed mutagenesis, and the production of
strand-specific probes.34-38 In this section, we focus on
investigating the 3′ f 5′ exodeoxyribonuclease activity of
Exo III, which involves specific binding to double-stranded
DNA followed by selective hydrolysis of one strand from
the DNA duplex. Figure 5a shows a schematic of the
strand-specific hydrolysis reaction of Exo III on a DNA
microarray. A two-component array was fabricated. (i)
DNA probe D1, which is surface-tethered via thiol modification of the 3′ end and (ii) the second DNA sequence D2
acts as a control probe and is 5′ thiol modified. Exo III will
specifically bind to the dsDNA, but not to the singlestranded DNA, and start converting dsDNA molecules to
ssDNA. The Exo III enzyme reaction can therefore be used
to identify hybridization adsorption onto ssDNA microarrays. The Exo III enzyme will not digest the other DNA
strand (DNA probe D1) in the duplex because the 3′ end
of this DNA strand is attached to the surface. An advantage
of this approach is that the DNA array can be used
repeatedly by simply denaturing any remaining dsDNA
with urea and rinsing with buffer.
In a first step, a two component ssDNA array (D1 and
D2) is exposed to the target complementary DNA sequence
(C1) resulting in duplex formation of D1 array elements.
Figure 5b shows an SPR difference image obtained after
a 500 nM solution of C1 was introduced to the DNA array
at room temperature (25 °C). An increase in the ∆%R was
observed only on D1 elements, indicating sequence-specific
hybridization adsorption and the formation of dsDNA on
the surface. Upon Exo III injection onto the array, the
enzyme selectively binds to the 3′ end of C1 in the D1-C1
duplex and sequentially releases 5′-mononucleotides into
the bulk solution. Figure 5c shows a difference image after
exposure to an 80 nM solution of Exo III for 40 min. It can
(34) Weiss, B. In The enzymes, 3rd ed.; Boyer, P. B., Ed.; Academic
Press, Inc.: New York, 1981; Vol. 14, pp 203-231.
(35) Okano, K.; Kambara, H. Anal. Biochem. 1995, 228, 101-108.
(36) Mol, C. D.; Kuo, C.; Thayer, M. M.; Cunningham, R. P.; Tainer,
J. A. Nature 1995, 374, 381-386.
(37) Brakmann, S.; Lobermann, S. Angew. Chem., Int. Ed. 2002, 41,
3215-3217.
(38) Greenberg, M. M.; Weledji, Y. N.; Kim, J.; Bales, B. C.
Biochemistry 2004, 43, 8178-8183.
Surface Enzyme Kinetics for Biopolymer Microarrays
Figure 6. Plot showing the kinetic data obtained at various
reaction temperatures (20, 27, and 37 °C) for the hydrolysis of
dsDNA microarrays at an Exo III concentration of 80 nM. The
semilogarithmic time plot is used to highlight differences during
the initial stages of the enzymatic reaction.
be clearly seen that Exo III has hydrolyzed C1 strands
from the D1-C1 duplex but has not affected the singlestranded D2 array elements. Moreover, the Exo III did
not affect the D1 ssDNA, so this hybridization/hydrolysis
cycle could be repeated up to 20 times without any
significant degradation in the SPR imaging signal. Additionally, in both reaction steps, nonspecific binding of
C1 or enzyme to either the D2 control spots or the PEG
background was not observed. The complete recovery of
the ∆%R signal to initial values at higher enzyme
concentrations also confirms that after hydrolysis the
enzyme does not remain on the array surface.
B. Temperature Dependence. Temperature is known
to play a significant role in determining the level of
exonuclease activity of Exo III. For example, between 22
and 46 °C, Exo III activity in solution increases proportionally with temperature, doubling approximately every
6 °C.39 Figure 6 shows real-time SPR imaging data
obtained at various reaction temperatures for a bulk
enzyme concentration of 80 nM. In each case, the SPR
signal was normalized with respect to the magnitude of
the ∆%R associated with the hybridization reaction step.
The time axis is plotted on a logarithmic scale to highlight
prominent differences during the early reaction stages.
The time scale required for complete cleavage of the dsDNA
microarray varied markedly, with values of 150, 490, and
1700 s measured at 37, 27, and 20 °C, respectively. At an
enzyme concentration of 80 nM, the rate of complete
removal of a 20-mer DNA strand can be estimated to be
8, 2.5, and 0.7 nucleotides/min at 37, 27, and 20 °C,
respectively. This is much lower than the range of 100600 nucleotides/min at 25-41 °C measured in solution
for a saturating enzyme concentration of 120 U Exo III/µg
DNA.39 The large variation between surface and bulk
cleavage rates can be attributed to a reduction in steric
freedom at the surface. As in the solution measurements,
the large variation in surface enzyme reaction times
reflects the strong dependence of Exo III surface activity
on temperature.
It is important to note that the SPR signal is the sum
of two componentssan increase due to enzyme adsorption
and a loss due to substrate cleavage. The measured SPR
signal increases initially in response to the ES complex
formation but eventually decreases significantly due to
the loss of the C1 complementary DNA sequence. At 37
°C, no net increase in the SPR signal was observed during
the early reaction stages. This suggests that the rate of
loss of surface bound species remains greater than the
rate of ES formation throughout the whole reaction period.
(39) Hoheisel, J. D. Anal. Biochem. 1993, 209, 238-246.
Langmuir, Vol. 21, No. 9, 2005 4055
At lower temperatures (27 and 20 °C), a pronounced initial
rise in signal is observed, suggesting that the rate of
enzyme adsorption must exceed the rate of duplex cleavage
over the same initial period. It is noted that a significant
increase in the activation energy associated with solution
exonuclease activity has been reported39 to occur at
temperatures below 25 °C. Additionally, higher processivity, which alludes to the average number of individual
nucleotides sequentially cleaved in a single enzymatic
action, also plays a much more prominent role at lower
temperatures.40 Therefore, it is reasonable to expect that,
due to the lower catalytic activity, the average residence
time of an enzyme molecule on the surface in the form of
the ES complex will be considerably longer at lower
temperatures, thus contributing to the observed initial
increase in SPR imaging signal.
C. Analysis of Exo III Reaction at 20°C. To achieve
further insight into the relative contributions of the
enzymatic adsorption and cleavage steps toward the
overall reaction rate, kinetics data were acquired using
several enzyme bulk concentrations at a fixed temperature
of 20 °C. The data were then analyzed by applying the
model introduced previously in Section II. Here, the
changes in the relative surface coverages of the ES complex
(θES) and the cleaved ssDNA product (θS*) over the reaction
course are controlled using three different parameters,
ka, kd, and kcat. The time-dependent SPR signal (∆%R) is
normalized with respect to the magnitude of ∆%R associated with the hybridization reaction step. The normalized signal responds to both enzyme adsorption and
surface loss of the C1 DNA complement and can be
represented by
∆%R(t) ∝ AθES - θS*
(19)
where A is a weighting factor. This is necessary to consider
since Exo III has a molecular weight (28 000 Da) considerably larger than the C1 DNA complement (6447 Da).
This suggests a weighting factor of around 4; however, it
must be noted that the surface density of the DNA duplex
monolayer is much higher than the surface enzyme
coverage. Additionally, differences in the binding affinity
of the ES complex and the D1-C1 duplex may have an
impact on their relative SPR signal contributions. When
analyzing our data, we applied weighting factor values
ranging from 1 to 4 and found the best model fit using a
value of A ) 1. Additional fluorescence measurements12,16
would allow us to ascertain the value of the weighting
factor.
Figure 7 compares theoretical analysis and experimental measurements when a 320 nM Exo III solution is
continually passed over a prepared dsDNA microarray at
20 °C. A global curve fitting approach was adopted to
simultaneously analyze a series of experimental curves
acquired at several different enzyme concentrations and
to determine the best values for the three model parameters (ka, kd, and kcat). By applying eqs 5-7 and 19, values
of ka ) 2.2 × 105 M-1‚s-1, kd ) 0.056 s-1, and kcat ) 0.009
s-1 were obtained. Using these values, the Langmuir
adsorption coefficient (KAds) is 3.9 × 106 M-1 and the surface
Michaelis-Menten constant (K′M) in eq 9 is 300 nM. The
simulated SPR signal using these values for an enzyme
concentration of 320 nM is shown in Figure 7b. It is clear
that there is a very good agreement between the measured
and simulated SPR signals.
Simulated plots of the different relative surface coverages are also presented in Figure 7. At an enzyme
(40) Kow, Y. W. Biochemistry 1989, 28, 3280-3287.
4056
Langmuir, Vol. 21, No. 9, 2005
Figure 7. (a) Theoretical analysis of the enzyme reaction using
eqs 5-7 and ka) 2.2 × 105 M-1‚s-1, [E] ) 320 nM, kd ) 0.056
s-1, and kcat ) 0.009 s-1. The steady-state value for λES is 0.54.
(b) The real-time SPR response (O) obtained for Exo III (320
nM) cleavage reaction onto D1 dsDNA array elements at 20 °C.
The dsDNA array was created by sequence-specific hybridization of C1 complementary sequences to two-component ssDNA
arrays composed of D1 and D2. The solid line represents the
simulated kinetic curve fitted using eqs 5-7 and 19 with the
same ka, kd, and kcat values reported above.
concentration of 320 nM, ka[E] ) 0.07 s-1, which is eight
times greater than kcat. The relative surface coverage of
ES (θES) quickly rises compared to the rate of C1 loss (θS*)
before reaching a maximum of 0.46 and slowly decreasing.
λES rises to a steady-state value of 0.54, which is about
equal to the calculated steady-state Langmuir isotherm
equilibrium value (θeq
ES in eq 11) of 0.56. The closeness of
these values indicates a significant but varying enzyme
coverage in the form of the ES complex, as expected from
Figure 4. When kcat is increased with respect to ka[E] (by
either increasing the reaction temperature to 37 °C or
decreasing [E]), λES will reach a steady-state value lower
than 0.54, reflecting a reduced intermediary ES complex
surface coverage.
The experimental and corresponding theoretical curves
obtained for enzyme concentrations varying from 50 to
320 nM are summarized in Figure 8. All the simulated
curves use the same values of ka, kd, and kcat quoted above.
The experimental data shown in this figure were obtained
using the same microarray by recovering the original
ssDNA surface through the use of urea to denature any
remaining duplex and rinsing with buffer between concentration runs. The measured SPR kinetic responses were
successfully analyzed with the theoretical model over the
entire range of enzyme concentrations studied. The ability
of the expected model to fit the data can be further tested
by examining T50%, the time at each curve associated with
50% depletion of single-stranded complementary (C1) from
the duplex monolayer, as a function of enzyme concentration. Figure 9 plots experimental data (O) and the values
calculated from the theory (2). A series of repeated
measurements at 20 °C using the same batch of enzyme
showed an excellent reproducibility of T50% ) (5% over
a number of chips prepared in an identical manner. The
dependence of T50% on [E] varies more rapidly at lower
enzyme concentrations (below 100 nM). The theory
predicts that at very high enzyme concentrations (g5 µM)
T50% approaches a value of 156 s. This value depends on
ka, kd, and kcat. The excellent fit of theory and experiment
in thisfigure clearly shows that the model constructed
Lee et al.
Figure 8. Top: Compiled experimental kinetic data obtained
at various concentrations of Exo III for the hydrolysis of D1-C1
duplexes at a temperature of 20 °C. The enzyme concentrations
(a, b, c, and d) are 50, 80, 160, and 320 nM, respectively.
Bottom: Simulated kinetic curves of the enzyme reaction fitted
using eqs 5-7 and 19 at the same enzyme concentrations as
in (a, b, c, and d) with the parameters ka) 2.2 × 105 M-1‚s-1,
kd ) 0.056 s-1, and kcat ) 0.009 s-1.
Figure 9. Plot of reaction times at 50% of observed SPR signal
decrease (T50%) versus Exo III enzyme concentrations. (O) is
the experimental data and (2) represents the calculated values
from the simulated data in Figure 8. The arrow represents the
limiting T50% value predicted by theory at very high enzyme
concentrations (g5 µM).
quantitatively describes the surface enzyme reaction and
emphasizes the importance of the coupling of enzyme
adsorption and surface reaction kinetics on the observed
reaction rate.
V. Conclusions
In this paper, we introduced a kinetic model that can
be used to analyze real-time kinetic measurements of
surface enzymatic activity using the technique of SPR
imaging. By combining the concepts associated with
Langmuir adsorption kinetics and Michaelis-Menten
analysis, it is possible to characterize the enzymatic
reaction in terms of three simple parameters (ka, kd, and
kcat). In classical Michaelis-Menten studies where the
substrate concentration is typically far in excess of the
enzyme concentration, the concentration of the intermediary ES complex (θES) can be assumed to be constant.
However, this assumption cannot be applied to surface
reactions where the substrate surface concentration is
finite and eventually goes to zero as the reaction is
completed. Instead, the fractional ES surface coverage of
unreacted sites (λES) reaches a constant value during the
course of the surface enzyme reaction.
Surface Enzyme Kinetics for Biopolymer Microarrays
The importance of the relative magnitudes of the rate
of adsorption (ka[E]) and catalysis (kcat) on the overall
reaction rate was demonstrated by studying the 3′ f 5′
cleavage activity of Exonuclease III on dsDNA microarrays. The experiments at 20 °C show that the value of λES
is comparable to the Langmuir equilibrium value (θeq
ES).
In contrast, λES becomes smaller at higher temperatures
due to increases in kcat. Further analysis of the Exo III
reaction at 37 °C will be discussed in a subsequent paper.
Finally, the surface exonuclease reaction analyzed in
this paper represents only one of many possible enzymatic
reactions that can be incorporated into the multiplexed
surface biosensor array format. Enzymes such as proteases, kinases, and ligases can all be used to manipulate
surface populations of biomolecules in order to achieve
higher sensitivity or specificity in bioassays. The analysis
of the Exo III surface reactions described in this paper
clearly shows that a coupled approach combining both
enzyme adsorption kinetics and enzymatic surface ca-
Langmuir, Vol. 21, No. 9, 2005 4057
talysis rates is required to quantitatively understand
surface enzymatic activity. Future work will focus on the
application of similar kinetic models to other surface
enzyme reactions. The very simple model proposed here
applies only to systems where the enzyme binds specifically to a surface target in a 1:1 interaction in the absence
of mass transport limitations. More complex models
involving, for example, multiple binding sites, such as a
transcription factor protein or lateral surface diffusion
between binding partners in membranes, will be required
for the analysis of more complex biochemical surface
processes.
Acknowledgment. This research is funded by the
National Institute of Health (2RO1 GM059622-04), the
National Science Foundation (CHE-0133151), and a startup grant from University of California, Irvine.
LA046822H